Prediction of Final Football League Standings by Dynamic Frontier Estimation

2017 ˙ IKE YILMAZ MEL SI UNIVERSITY IS¸IK BY DYNAMIC FRONTIER ESTIMATION PREDICTION OF FINAL FOOTBALL LEAGUE STANDINGS

MELIKE˙ YILMAZ M.S. Thesis 2017 PREDICTION OF FINAL FOOTBALL LEAGUE STANDINGS BY DYNAMIC FRONTIER ESTIMATION

MELIKE˙ YILMAZ B.S., Industrial Engineering, IS¸IK UNIVERSITY, 2015

Submitted to the Graduate School of Science and Engineering in partial fulﬁllment of the requirements for the degree of Master of Science in Industrial Engineering Operations Research

IS¸IK UNIVERSITY 2017 IS¸IK UNIVERSITY GRADUATE SCHOOL OF SCIENCE AND ENGINEERING

PREDICTION OF FINAL FOOTBALL LEAGUE STANDINGS BY DYNAMIC FRONTIER ESTIMATION

MELIKE˙ YILMAZ

APPROVED BY:

Assist. Prof. Dr. S. Tankut Atan I¸sıkUniversity (Thesis Supervisor)

Assoc. Prof. Dr. S. C¸a˘glarAksezer I¸sıkUniversity (Thesis Co-Supervisor)

Assist. Prof. Dr. Demet O.¨ Unl¨uakın¨ I¸sıkUniversity

Assist. Prof. Dr. Burak C¸avdaro˘glu Kadir Has University

APPROVAL DATE: ..../..../.... PREDICTION OF FINAL FOOTBALL LEAGUE STANDINGS BY DYNAMIC FRONTIER ESTIMATION

Abstract

Data Envelopment Analysis (DEA) is a commonly used method for efficiency assessment of teams in many sports including football. In this work, we investigate how estimations of final league standings with DEA efficiency measures evolve as the season progresses using Turkish first division football league data for five seasons. After the conclusion of each week, a DEA analysis is run using available data until then, and computed efficiencies are used to estimate the final table standings. While the estimates fluctuate early in the season, they tend to stabilize after several weeks. Tracking the weekly progress of the results may give the teams a chance to finish in a better position by focusing on their inefficiencies. Furthermore, the choice of the DEA linear programming model makes a difference in the quality of the results. Estimations are improved by using a model that incorporates expert knowledge about football.

Keywords: Data Envelopment Analysis (DEA), Assurance Region Model, Football Eﬃciency, Turkish Football Clubs

ii DINAM˙ IK˙ ONC¨ U¨ METOTLAR KULLANARAK FUTBOL LIG˙ IN˙ IN˙ PUAN SIRALAMASININ TAHMIN˙ I˙

Ozet¨

Veri Zarflama Analizi (VZA) metodu, futbol dahil olmak üzerebir¸coktakım sporunun verimlilik de˘gerlendirmesi i¸cinyaygın olarak kullanılmaktadır. Bu ¸calı¸s- mada, Türkiye’de birinci ligde oynayan futbol takımlarının performansları son be¸syıllık ger¸cekveri ile analiz edilip de˘gerlendirilmektedir. Çalı¸smanın amacı, performans özelliklerini kullanarak lig sonunda olu¸sması muhtemel sıralamayı sezon i¸cerisindeolabildi˘ginceerken tahmin etmektir. Sezonun ba¸sındaki tahmin do˘grululuk oranı dü¸sükolurken, sezon haftaları ge¸ctik¸cekayda de˘gerse- viyelere ¸cıkmaktadır. Yapılan haftalık analizler sonrasında, her karar noktası yani takımın etkinlik de˘gerihakkında bilgiler elde edilmektedir. Bu bilgiler kul- lanılarak takımların zayıf yönlerineyönelikhamleler yapması ve sezonu daha iyi bir sırada bitirmesi mümkünolacaktır.

Anahtar kelimeler: Veri Zarflama Analizi (VZA), Güven Bölgesi (AR) Yöntemi, Futbol Verimlili˘gi,Türkiye Futbol Kulüpleri

iii Acknowledgements

First of all, I would like to give special thanks to my thesis supervisor Assist. Prof. S. Dr. Tankut Atan for his great concern, patience, kind support and guidance. I would like to also give special thanks to my thesis co-supervisor Assoc. Prof. S. Dr. C¸a˘glarAksezer, for his never ended patience, support and guidance. It was pleasure working with them during my master studies.

Additionally, I would like to also thank all other faculty members of I¸sıkUniversity Industrial Engineering Department for their support during my bachelor and master studies.

Special appreciation goes to my friends and colleagues who have provided support to me in completing my study.

Also, I am extremely gratefully to thank to my parents G¨uzideYılmaz, Umit¨ Yılmaz, Umit¨ Can Yılmaz and S¸ehnaz Ozel¨ for their never ended trust, patience and endless encouragement.

iv To my family and friends. . . Table of Contents

Abstract ii

Ozet¨ iii

Acknowledgements iv

List of Tables vii

List of Figures viii

List of Abbreviations ix

1 Introduction 1

2 Literature Review 4

3 Data 11

4 Methodology 15 4.1 Data Envelopment Analysis (DEA) ...... 15 4.2 Analytic Hierarchy Process (AHP) ...... 22

5 Results 27 5.1 Financial Data ...... 34

6 Conclusion 36

Reference 39

Appendices 45

A 46 A.1 Data ...... 46 A.2 Analytic Hierarchy Process ...... 52 A.3 Pearson Correlation Coeﬃcients Results ...... 56 List of Tables

2.1 Review of the literature on performance assessment of football teams using DEA...... 7 2.2 Review of the literature on performance assessment of basketball and handball teams using DEA...... 8 2.3 Review of the literature on performance assessment of tennis and olympic games using DEA...... 9 2.4 Review of the literature on performance assessment of baseball, handball and golf teams using DEA...... 10

3.1 Descriptive statistics...... 14

4.1 Results of a numerical example from 2015-2016 season...... 20 4.2 Saaty’s nine-point scale for relative importance...... 22 4.3 Geometric mean matrix...... 23 4.4 Normalized matrix...... 23 4.5 Priorities of the inputs by the experts...... 26 4.6 Assurance Region lower and upper bounds for input ratios. . . . . 26

5.1 Descriptive statistics of CCR and AR models...... 31 5.2 Descriptive statistics of ﬁnancial data...... 35

A.1 Sample data. Week 34 in 2011-2012...... 46 A.2 Sample data. Week 34 in 2012-2013...... 47 A.3 Sample data. Week 34 in 2013-2014...... 48 A.4 Sample data. Week 34 in 2014-2015...... 49 A.5 Sample data. Week 34 in 2015-2016...... 50 A.6 Correlation coeﬃcient matrix...... 51 A.7 Comparison matrix for the inputs by Expert 1...... 52 A.8 Comparison matrix for the inputs by Expert 2...... 52 A.9 Comparison matrix for the inputs by Expert 3...... 53 A.10 Comparison matrix for the inputs by Expert 4...... 53 A.11 Comparison matrix for the inputs by Expert 5...... 54 A.12 Random Index Table...... 54 A.13 Regression on rank: Final league standings vs. DEA estimations (R-square %) results...... 56 A.14 Regression on rank: Weekly league standings vs. DEA estimations (R-square %) results...... 57

vii List of Figures

4.1 Eﬃciency graph of 2015-2016 season...... 21

5.1 Regression on rank: Final league standings vs. DEA estimations. . 30 5.2 Weekly vs. ﬁnal league rank estimation...... 32 5.3 Progress of DEA scores for various cases...... 33 5.4 Financial analysis of football teams for ﬁve seasons...... 34

A.1 AHP questionnaire...... 55

viii List of Abbreviations

AHP Analytical Hierarcy Process AR Assurance Region AR-I-C Input Oriented Assurance Region Model CCR Charnes Cooper Rhodes CCR-I Input Oriented Charnes Cooper Rhodes Model CI Consistency Index CR Consistency Ratio CRS Constant Returns to Scale DEA Data Envelopment Analysis DMU Decision Making Unit LP Linear Programming NBA National Basketball Association NFL National Football League RI Random Consistency Index SFA Stochastic Frontier Analysis TFF Turkish Football Federation UEFA Union of European Football Associations VRS Variable Returns to Scale

ix Chapter 1

Introduction

Besides being the most popular sport in terms of followers and fans, football is a multibillion dollar industry that dominates the sports economics. Without doubt, European football clubs and managing bodies are the prominent stakeholders of this industry. Szymanski [1] provides a diverse collection of challenges faced in this arena since early 90’s, especially focused on Euro area. European football holds several ﬁnancial earning records for any professional sport on the face of the planet. According to Harris [2] , United Kingdom (UK) Premier League is the most broadcasted league in the world with earnings from TV rights of more than $2.5 billions per year being second best only after NFL. It also holds several top spots in the list of international clubs with most expensive sponsorship deals signed. Teams from UK and Spain are earning vast sums of money from selling their jersey and arena naming rights. More importantly, record amount of prize money is distributed to competitor clubs through organizations such as European Football Associations (UEFA) Champions League with total prize money well over billion dollars.

In order to get a larger slice of the cake, teams try to achieve higher international recognition and dominance over each other. Consecutive appearances in international organizations is the major key to this success. Teams qualify for such organizations when they secure a certain top spot in their ﬁnal national league

1 standing. Turkish national league, which is named ”Spor Toto Süper Lig”, con- tains 18 top division clubs. A total 34 home and away games are played by each team with a Federation Cup tournament. Champion of the league is directly qualified for UEFA Champions League; the runner up should plays certain rounds of qualification matches. A certain number of consecutive seeders are qualified for the UEFA Europa League, which is the other international organization with slightly less prestige and financial earnings.

Turkey’s football industry gained critical acclaim during recent years as it improves drastically in terms of financial winning and losses. An in-depth historical background of Turkish football is provided by Senyuva and Tunc [3]. Clubs have earned large amounts of money from the sale of broadcasting rights and gained higher fan attendance as the construction of new generation stadiums completed. On the other hand, they also faced massive budgetary deficits because of operating losses mainly occurring from astronomic transfer fees. Some of the clubs were even banned from international organizations because of the regulatory financial play rules. Some studies suggest that these economical factors have socio- psychological impacts on the society as well. Berument and Yücel[4] provide the statistical basis of relation between Turkish industrial production performance and field performance of the country’s most popular club, Fenerbah¸ceSK. It is shown that Fenerbah¸ce’sinternational wins have a significant effect on the industrial growth where for domestic successes an insignificant effect has been observed. McManus [5] claims that rapid commercialism and commodification of Turkish league football has affected the activities of club supporter groups. A case on Be¸sikta¸sJK, league champion of 2016, implies a change in fan groups’ actions moving beyond football, and groups gaining a status as an ethical and political body, especially with support of social media. Other studies on Turkish clubs by means of economical indicators such as liquidity, liability, profitability and stock performance can be found in Berument et al. [6] and Ecer and Boyukaslan [7].

This study provides a blueprint for weekly performance assessment of competing teams and an estimation scheme of the ﬁnal standings at the earliest time horizon

2 in the fixture. Due to its financial implications, a good guess about a team’s final standing is important at any point during the league’s progress should the team continue to perform as it did until then. This also gives a team the chance of improving its inefficiencies in the rest of the season to attain a better standing. An empirical analysis on Turkish Süper Lig is illustrated by using Data Envelopment Analysis (DEA), a very popular non-parametric frontier estimation technique. It is also shown that a model incorporating expert knowledge performs better.

Rest of the thesis is organized as follows. A review of the existing literature relevant to our work is presented in Chapter 2. Then, Chapter 3 presents the data which we used on our models as inputs and outputs. Later then Chapter 4 describes the methodology and explains mathematical models. Chapter 5 presents the empirical results obtained with DEA analysis and ﬁnally Chapter 6 concludes the thesis.

3 Chapter 2

Literature Review

DEA has been widely used to assess the performance of football related activities with a variety of performance indicators. Haas [8] investigated the technical and scale efficiency of football teams in the English Premier League, took the playing talent and the coaching capabilities available to a team as inputs. The outputs included the points won and total revenues, while taking the population size of the home town as a non-discretionary input. Haas [9] investigated the technical efficiency of soccer teams in the Major League Soccer bearing in the mind that players’ wage bill and wage of the head coach as inputs, and points awarded, absolute number of spectators and revenues as outputs. Haas et al. [10] studied the efficiency of football teams in the German Bundesliga considering players’ wage bill and wage of the head coach as inputs, and points awarded, total revenues and average stadium utilization as outputs.

Bosca et al. [11] analyzed offensive and defensive efficiency of Italian and Spanish football teams to shed light on the sport performance. The offensive inputs include shots-on-goal, attacking plays made by the team, balls kicked into the opposing team’s goal area and minutes of possession while the defensive inputs are the inverse of the offensive inputs. The offensive output is number of goals scored while the defensive output is the inverse of the number of goals conceded. First, DEA model compares these inputs with the output to establish which team is more efficient. Secondly, using regression analysis the authors explain how the

4 points obtained by the teams correspond to different indicators to decide which one is more important to be efficient offensively or defensively, and to obtain a high ranking in the league.

Espitia-Escuer and Garcia-Cebrian [12] measured the efficiency of the professional soccer teams that play in the Spanish First Division taking the players used, attacking moves, the minutes of possession of the ball and the shots and headers as input variables; as output, they considered the number of points achieved. Espitia-Escuer and Garcia-Cebrian [13] examined the Total Factor Productivity evolution of Spanish First Division Football teams using the Malmquist Index. Garcia-Sanchez [14] applied a three-stage-DEA model to Spanish Professional Football League separating the teams’ economic behavior into three components: operating efficiency, athletic or operating effectiveness, and social effectiveness. Guzman and Morrow [15] studied the efficiency of clubs in the English Premier League and used Malmquist non-parametric technique to measure changes in efficiency and productivity. They also used DEA with Canonical Correlation Analysis to ensure the cohesion of the input and output variables.

Soleimani-Damaneh et al. [16] utilized input-oriented weight-restricted DEA technique for evaluating the performance of the teams in the Iranian primary football league. They engaged Analytical Hierarchy Process (AHP) for aggregating the subfactors which are involved in input factors, then calculated the eﬃciency measures with DEA. In addition, with AHP they constructed weight restrictions for increasing the discrimination power of the DEA model. Zambom-Ferraresi et al. [17] evaluated the sports performance of teams competing in the UEFA Champi- ons League. They used a bootstrap DEA model considering inputs ad attempts on target, ball possession, total passes and ball recoveries, and sports results as output.

Focusing on match efficiencies rather than teams’, Villa and Lozano [18] assess the scoring efficiency of each football match in the season. By averaging these match efficiencies they compute teams’ scoring efficiencies for the season and

5 find a virtual final league table as well. Since the proposed DEA models can be run after each match, the changes in efficiency can be monitored throughout the season similar to what we propose in our study. They applied their approach to Spanish First Division teams for one season only. The other articles about football efficiency can be found in Table 2.1.

Several applications of DEA for sport performance evaluation can be found such as Cooper et al. [19] for basketball players, Lewis et al. [20] for Major League Basketball teams, Amin and Sharma [21] for cricket team selection among others. Articles about DEA for performance evaluation in sports other than football can be found in Table 2.2 through 2.4.

6 Table 2.1: Review of the literature on performance assessment of football teams using DEA. Football Papers Methodology Inputs Outputs Ascari CCR model Ball possession Goal Gapnepain [22] BCC model Wages Shots Red cards Points Town population Barros Bootstrap DEA Operational cost Attendance Garcia-del-Barrio Team payroll Other receipts [23] Total assets Barros et al. [24] Bootstrap DEA Operational cost Attendance Total assets Points awarded Team payroll Total receipts Barros CCR model Players Turnover Leach [25] BCC model Wages Points Net assets Attendance Stadium facilities Guzman [26] DEA Staﬀ costs Turnover Malmquist Po- General expenses ductivity Index Kounetas [27] Bootstrap DEA Total players’ transfer Points expenses and contract renewals Operational costs Total attendance Picazo-Tadeo DEA Number of players Points awarded Gonzalez-Gomez Attendance (fans) Games played in [28] European competitions and King’s Cup Sala et al. [29] DEA window Attacks in area centre Goal scored analysis plays CCR-O model Attacks in area shots Inverse of goals re- on ceived

7 Table 2.2: Review of the literature on performance assessment of basketball and handball teams using DEA. Basketball Papers Methodology Inputs Outputs Aizemberg et al. BCC model Payroll Wins [30] Average attendance Average points per game Moreno Network DEA Team budget Number of team victories Lozano [31] Black-box DEA Lee and Berri [32] Stochastic Fron- Team wins Talent of guards tier Analysis SFA Talent of power for- ward and centers Hofler and Payne SFA Rebound, Assists Team wins (actual number) [33] Steals, Free throw Blocked shots Percentage of field goal Handball Papers Methodology Inputs Outputs Gutiérrez CCR model Constant input Number of goals scored (9m) Ruiz [34] Cross-efficieny Number of goals scored (6m) Fastbreak goals Assists Fouls Number of 7m caused Turnovers

8 Table 2.3: Review of the literature on performance assessment of tennis and olympic games using DEA. Tennis Papers Methodology Inputs Outputs Glass et al.[35] VRS First serves in (%) Season earnings Super-efficiency Points won on first Matches won (%) model serve (%) Points won on second serve (%) Average aces per match Inverse of average double faults per match Break points save (%) Service games won (%) Points won returning the first serve (%) Points won returning the second serve (%) Break points won (%) Returns games won (%) Tie breaks won (%) Olympic Games Papers Methodology Inputs Outputs Lozano VRS Gross National Prod- Number of gold uct medals Villa AR Population Number of silver medals Cortes [36] Number of bronze medals Wu Integer-valued Gross Domestic Prod- Number of gold DEA model uct medals Zhou Population Number of silver medals Liang [37] Number of bronze medals

9 Table 2.4: Review of the literature on performance assessment of baseball, handball and golf teams using DEA. Baseball Papers Methodology Inputs Outputs Anderson Composite Bat- At-bats Number of walks ter Index Sharp [38] CCR-I model Runs-batted-in Singles Fielding average Doubles Runs scored Triples Number of seasons Home runs played Porter and Scully LP model Hitting Percentage of wins [39] Pitching Depken [40] Fixed eﬀects Team winning per- Salary expenditure model centage Intrateam salary Kang et al.[41] CCR model Total player salary Winning percent Total fan attendance Cycling Papers Methodology Inputs Outputs Rogge et al. [42] Robust DEA- Number of cycling CQ points collected based eﬃciency quotient Team budget Prize money Number of tour starts Prizes Tour team consistency Golf Fried BCC model Driving distance Earnings per event Lambrinos Drives in fairway Tyner [43] Scrambling Greens hit in regula- tion Sand saves Number of putts per green

10 Chapter 3

Data

The data in this study have been collected from the official homepage of the Turkish Professional Football League web site [44] and a private organization FSTATS [45] with detailed statistics of Turkish Süper Lig Football Clubs in the years 2011/12 to 2015/16 (18 Clubs × 34 weeks × 5 seasons). Sample data for each season is shown in Tables A.1 through A.5. We begin by defining football’s output, and then verify out choice of inputs the analysis of DEA models. Scoring a goal in football is one of the most thrilling moments and determines the winner of the game. Thus, our output is the goal ratio; the number of goals scored divided by the number of goals conceded.

Determining the best performance indicators/variables to use in a DEA analysis is an open question. Furthermore, not all relevant data may be available publicly, or they may not even be collected so the researchers are restricted to data they can obtain. In addition, data sets involving football performance usually contain vast amounts of statistics and indicators belonging to each team. DEA faces a challenge when working with such a high number of performance indicators compared to relatively small number of decision making units. Drake and Howcroft [46] overcome this by stating a critical ratio in a rule of thumb manner as the number of the inputs and outputs should at least be twice greater than the decision units under investigation. Since we have a small number of decision making units, a correlation analysis has been performed in order to identify truly eﬀective

11 performance indicators and to eliminate redundancies. Resulting matrix containing the pairwise Pearson correlation coefficient shown in Table A.6 allows us to refine the inputs into a smaller subset. For example, number of assists and goal positions are highly correlated to each other with a correlation coefficient 0.82. A further elimination is done for the performance indicator free kicks. Although it could not be eliminated immediately due to low correlations with other variables, it was eliminated after applying the methodology explained in the study because it did not change the efficiency results at all.

Some researchers such as Haas et al. [10] have used data involving the economic value of each team in their team efficiency studies. Several resources for such data come to mind. One is transfer money paid to players. This money is agreed upon before the season starts and stays the same throughout the season. Thus, since we are trying to estimate final league standings after each week, transfer fees data cannot be used towards that end. Another financial indicator could have been stock values of the teams which actually change over time but most Turkish football clubs are not public. Attendance numbers also have financial implications and they have been used by other researchers such as Haas [9]. But in Turkey fans of teams have long been banned from away games by local authorities making such data irrelevant to our study. Nevertheless, in Section 5 we also give our findings obtained using transfer money data together with other data for the whole season in a static manner.

After this initial analysis of the data at hand, the number of goal positions, the number of shots on target, the number of crosses on target, the number of corner kicks and the ball possession percentage were our chosen inputs.

• Goal positions: This indicator is naturally related to the number of goals a team scores. In general, teams that perform better in the season produce more goal positions. The number of goal positions a team creates physically tires and psychologically demoralizes opposing teams.

12 • Shots on target: A shot is an attempt that is taken with the purpose of scoring and is directed toward the goal. A shot on target either results in a save by the goalkeeper/defending team, or a goal by the attacking team.

• Crosses on target: A cross is a high ball sent into the goal area with diﬀerent intensities. The most common cross is a ball sent from the corner lines towards the area in front of the goal. A good cross generates a threat for the opposing team because the fast incoming ball can be sent via foot or head into the goal without the defenders being able to react quickly enough.

• A corner kicks: A corner kick is awarded to the attacking team when the ball leaves the field of play by crossing the goal line either on the ground or in the air without a goal having been scored, having been last touched by a defending player. The kick is taken from the corners of the field nearest to where the ball crossed the goal line. Corner kicks are considered to be a reasonable goal scoring opportunity for the attacking side. It is even possible to score directly from a corner kick if sufficient swerve is given to the kick.

• Ball possession: Ball possession is the percentage of total game time where a team has the control of the ball. A high ball possession shows that a team dominates the game winning the match with a high likelihood.

The descriptive statistics of selected input and output variables for all analyzed seasons are provided in Table 3.1.

13 Table 3.1: Descriptive statistics. Inputs Output Shots Crosses Goal Corner Ball Goal Season on on positions kicks possession Ratio target target 2011-2012 Max 198 218 227 188 56 2.88 Min 95 108 111 133 41 0.29 Average 153.94 164.17 166.33 162.06 48.28 1.10 SD 29.64 29.21 31.01 15.89 4.07 0.56 2012-2013 Max 197 202 207 227 57 1.89 Min 114 101 122 129 45 0.58 Average 157.50 159.83 148.72 165.61 49.39 1.03 SD 24.12 26.34 22.34 24.86 3.93 0.32 2013-2014 Max 223 235 184 211 56 2.24 Min 142 127 101 137 45 0.53 Average 165.61 166.06 138.94 170 49.50 1.07 SD 23.56 25.95 24.73 19.12 3.47 0.46 2014-2015 Max 229 223 210 217 58 2.07 Min 126 136 104 114 40 0.65 Average 165.06 171.72 135.39 160.89 49.56 1.09 SD 32.01 25.68 27.93 26.48 3.94 0.45 2015-2016 Max 226 220 165 221 57 2.22 Min 103 124 73 120 46 0.44 Average 156.33 158.67 102.22 162.72 49.56 1.09 SD 33.54 29.31 25.90 27.84 3.38 0.51 Max= maximum; Min= minimum; SD= standard deviation.

14 Chapter 4

Methodology

Our methodology proceeds as follows. First, via DEA we find team efficiencies by utilizing the data through the week that has just been played. These team efficiencies are then used to predict final league standings of the teams. The predictions are dynamically renewed after each week. While we report results via a standard DEA model as well, we find out that a model that uses expert knowledge makes better predictions. To collect expert opinion, we use Analytic Hierarchy Process (AHP).

4.1 Data Envelopment Analysis (DEA)

Data Envelopment Analysis (DEA) first introduced by Charnes [47] is an opti- mization technique for evaluating the comparative efficiency of homogenous decision making unit (DMU), consuming inputs and transforming them into outputs. The term comparison is used because the evaluation is carried out relative to the DMUs present in the peer set. This comparison is performed by finding the efficiency of each DMU with respect to other DMUs with most efficient DMUs setting benchmarks.

We used Charnes, Cooper and Rhodes (CCR) input-oriented model (Cooper et al. [48]) for evaluating the eﬃciency of football teams (DMUs). This model aims to minimize inputs (or resources consumed) while satisfying at least the given

15 input levels. There exist several other DEA models that are actually variants of the original version given below. Let n be the number of DMUs, m be the number of inputs and s be the number of outputs. Let us assume that we have a data matrix containing the input and output values of DMUs with a size of n by m+s.

Then the fractional CCR model is formulated as below.

Ps r=1 uryr0 max θ = Pm (4.1) i=1 vixi0

subject to:

Ps r=1 uryrj Pm ≤ 1 j = 1, ..., n (4.2) i=1 vixij

ur, vi ≥ 0 r = 1, ..., s; i = 1, ..., m (4.3)

DEA model evaluates the eﬃciency score, θ, of DMU j0 with reference to all other n-1 DMUs where xij and yrj are the relevant input and output levels of DMU under evaluation from the data matrix. The positive weights of inputs and outputs are decision variables, and represented by ur and vi.

As solving the fractional is diﬃcult, it was converted to a linear programming (LP) model by Charnes et al. [47]:

s X max θ = uryr0 (4.4) r=1

subject to:

m X vixi0 = 1 (4.5) i=1

s m X X uryrj − vixij ≤ 0 j = 1, ..., n (4.6) r=1 i=1

16 ur, vi ≥ 0 r = 1, ..., s; i = 1, ..., m (4.7)

We illustrate a small numerical example of the CCR model (LP form).

The data for 2015-2016 season is shown in Table A.5. There are 18 DMUs with 5 inputs and 1 output. The following formulation belongs to team Fenerbah¸ce. max θ = 2.222u subject to:

2.222u-221v1-203v2-165v3-219v4-56v5 ≤ 0

1.024u-132v1-136v2-77v3-120v4-47v5 ≤ 0

1.000u-162v1-162v2-84v3-164v4-50v5 ≤ 0

1.500u-157v1-163v2-104v3-151v4-50v5 ≤ 0

2.143u-226v1-220v2-116v3-221v4-57v5 ≤ 0

0.855u-149v1-148v2-128v3-151v4-50v5 ≤ 0

0.813u-150v1-145v2-118v3-152v4-46v5 ≤ 0

0.619u-1311v1-144v2-76v3-146v4-47v5 ≤ 0

1.408u-206v1-207v2-119v3-170v4-55v5 ≤ 0

0.620u-103v1-124v2-73v3-124v4-47v5 ≤ 0

1.000u-133v1-131v2-89v3-148v4-46v5 ≤ 0

1.250u-176v1-186v2-117v3-174v4-50v5 ≤ 0

0.610u-139v1-137v2-83v3-181v4-48v5 ≤ 0

1.333u-133v1-131v2-77v3-135v4-48v5 ≤ 0

0.437u-119v1-126v2-83v3-155v4-48v5 ≤ 0

1.440u-167v1-177v2-80v3-189v4-46v5 ≤ 0

0.708u-163v1-150v2-115v3-178v4-51v5 ≤ 0

0.678u-147v1-166v2-136v3-151v4-50v5 ≤ 0

221v1+203v2+165v3+219v4+56v5=1 u,v1,v2,v3,v4,v5 ≥ 0

17 The computational eﬀort of linear programming is prone to grow in proportion to powers of the number of constraints. The number of DMUs, n, is quite larger than (m + s), the number of inputs and outputs and therefore it takes more time to solve LP which has n constraints than to solve dual problem which has (m + s) constraints. Moreover, the interpretations of dual problem are more comprehensible because the solutions are characterized as inputs and outputs that correspond to the original data whereas the multipliers provided by solution to LP represent evaluations of these observed values. These values are also important, they are generally best reserved for supplementary analysis after a solution to dual problem is achieved [48]. The dual of CCR model is:

min θ (4.8)

subject to:

n X λjxij ≤ θ0xi0 i = 1, ..., m (4.9) j=1

n X λjyrj ≥ yr0 r = 1, ..., s (4.10) j=1

λj ≥ 0 j = 1, ..., n (4.11)

The dual is illustrated below by a numerical example for team Fenerbah¸ce. min θ subject to:

132λ1+162λ2+157λ3+226λ4+149λ5+150λ6+131λ7+221λ8+206λ9+103λ10+133λ11

+176λ12+139λ13+133λ14+119λ15+167λ16+163λ17+147λ18 ≤ 211θ

136λ1+162λ2+163λ3+220λ4+148λ5+145λ6+144λ7+203λ8+207λ9+124λ10+131λ11

+186λ12+137λ13+131λ14+126λ15+177λ16+150λ17+166λ18 ≤ 203θ

18 77λ1+84λ2+104λ3+116λ4+128λ5+118λ6+76λ7+165λ8+119λ9+73λ10+89λ11+117λ12

+83λ13+77λ14+83λ15+80λ16+115λ17+136λ18 ≤ 165θ

120λ1+164λ2+151λ3+221λ4+151λ5+152λ6+146λ7+219λ8+170λ9+124λ10+148λ11

+174λ12+181λ13+135λ14+155λ15+189λ16+178λ17+151λ18 ≤ 219θ

47λ1+50λ2+50λ3+57λ4+50λ5+46λ6+47λ7+56λ8+55λ9+47λ10+46λ11+50λ12+48λ13

+48λ14+48λ15+46λ16+51λ17+50λ18 ≤ 56θ

1.024λ1+1.000λ2+1.500λ3+2.143λ4+0.855λ5+0.813λ6+0.619λ7+2.222λ8+1.408λ9

+0.620λ10+1.000λ11+1.250λ12+0.610λ13+1.333λ14+0.437λ15+1.440λ16+0.708λ17

+0.678λ18≥ 2.222

λ1+λ2+λ3+λ4+λ5+λ6+λ7+λ8+λ9+λ10+λ11+λ12+λ13+λ14+λ15+λ16+λ17+λ18≥ 0

After writing all these equations for each team (DMUs), then we solved CCR model for 2015-2016 season by using DEA-Solver Pro [49]. The results of this example are shown in Table 4.1. There are three efficient teams which are Be¸sikta¸s, Fenerbah¸ceand Konyaspor and the rest are inefficient teams. By looking at the efficiency scores for all DMUs, we can understand how much inefficient units need to reduce their inputs or increase their outputs to become efficient. The efficiency graph is shown in Figure 4.1 .

∗ ∗ In CCR model, the optimal weights (ur, vi ) for ineﬃcient DMUs may result in many zeros implying weakness in the corresponding items compared with eﬃcient DMUs. Additionally from Table 4.1 one can see that two important inputs in football, shots on target and number of corner kicks, have zero weights for almost all teams. To get rid of zero weights which frequently appear in CCR model, we used the Assurance Region (AR) model developed by Thompson et al. [50]. In AR model, lower and upper bounds are set for ratios of input and output variables. Thus, the model has the following additional constraints over CCR model.

19 vi 0 0 0 lbi,i0 ≤ ≤ ubi,i0 i = 1, ..., m; i = 1, ..., m; i 6= i ; i < i (4.12) vi0

ur 0 0 0 LBr,r0 ≤ ≤ UBr,r0 r = 1, ..., s; r = 1, ..., s; r 6= r ; r < r (4.13) ur0

where lbi,i0 (ubi,i0 ) are lower (upper) bounds on the ratios of input weights and

LBr,r0 (UBr,r0 ) are the lower (upper) bounds on the ratios of output weights.

Table 4.1: Results of a numerical example from 2015-2016 season. Teams Score V(1) V(2) V(3) V(4) V(5) (U1) Akhisar 0.85 0.00 0.00 0.04 0.02 0.00 0.83 Belediyespor Antalyaspor 0.65 0.12 0.00 0.18 0.00 0.00 0.65 Ba¸sak¸sehir 0.99 0.00 0.00 0.03 0.20 0.00 0.66 Be¸sikta¸s 1.00 0.08 0.00 0.13 0.00 0.00 0.47 Bursaspor 0.57 0.23 0.00 0.00 0.00 0.00 0.67 C¸aykur Rizespor 0.54 0.23 0.00 0.00 0.00 0.00 0.66 Eski¸sehirspor 0.47 0.19 0.00 0.06 0.00 0.00 0.77 Fenerbah¸ce 1.00 0.15 0.00 0.00 0.00 0.00 0.45 Galatasaray 0.82 0.00 0.00 0.03 0.18 0.00 0.58 Gaziantepspor 0.60 0.33 0.00 0.01 0.00 0.00 0.97 Gen¸clerbirli˘gi 0.75 0.25 0.00 0.01 0.00 0.00 0.75 Kasımpa¸sa 0.72 0.00 0.00 0.04 0.16 0.00 0.57 Kayserispor 0.44 0.18 0.00 0.06 0.00 0.00 0.72 Konyaspor 1.00 0.25 0.00 0.01 0.00 0.00 0.75 Mersin 0.36 0.28 0.00 0.01 0.00 0.00 0.84 Idmanyurdu˙ Osmanlıspor 0.98 0.00 0.00 0.43 0.00 0.00 0.68 Sivasspor 0.44 0.00 0.17 0.07 0.00 0.00 0.62 Trabzonspor 0.46 0.23 0.00 0.00 0.00 0.00 0.68 V(1);V(2);V(3);V(4);V(5) are the weights of the inputs, U(1) is the weight of the output.

20 21

Figure 4.1: Eﬃciency graph of 2015-2016 season. 4.2 Analytic Hierarchy Process (AHP)

To determine AR bound values we used Analytic Hierarchy Process (AHP) which was developed by Saaty [51] to deal with complex decision making. AHP may help the decision maker to set priorities and make the best decision by reducing complex decisions to a series of pairwise comparisons and then synthesizing the results. Moreover, AHP is a practical technique for checking the consistency of the decision makers’ pairwise comparisons of the criteria. AHP is conducted through a questionnaire answered by area experts. Example questionnaire is shown in Figure A.1.

In this study, the questionnaire was administered to ﬁve football players to identify their expert opinion about relative importance of criteria that aﬀect team performances. Respondents were asked to conduct pairwise comparisons among the input variables on a 1 to 9 scale as in Saaty [52].

The nine-point scale is shown in Table 4.2.

Table 4.2: Saaty’s nine-point scale for relative importance. Importance Deﬁnition Explanation Level 1 Equal importance Two criteria play a role equally Judgement slightly support one 3 Moderate importance criterion over another Judgement strongly support one 5 Strong importance criterion over another Judgement is supported very 7 Very strong importance strongly over another The argument supporting one 9 Extreme importance criterion over another When compromise is between 2,4,6,8 Intermediate values two adjacent needed judgement

The first step is the pairwise comparison for the inputs by five experts shown in Table A.7 through A.11. Then, we calculate the geometric mean of pairwise comparison matrix for the inputs by five experts shown in Table 4.3.

22 Table 4.3: Geometric mean matrix. Goal Shots on Crosses on Corner Ball Positions Target Target Kicks Possession Goal 1.0000 1.4768 4.5844 8.0018 5.0776 Positions Shots on 0.6776 1.0000 7.7403 8.1393 1.8384 Target Crosses on 0.2181 0.1292 1.0000 2.7131 1.6345 Target Corner 0.1250 0.1229 0.3505 1.0000 0.2717 Kicks Ball 0.1969 0.5439 0.6118 3.6801 1.0000 Possession SUM 2.2177 3.2718 14.2870 23.5343 9.8222

The second step is to normalize the matrix by totaling numbers in each column. Each entry in the column is divided by the column sum to yield its normalized scores shown in Table 4.4. The sum of each column should be 1.

Table 4.4: Normalized matrix. Goal Shots on Crosses Corner Ball Pos- Average Positions Target on Target Kicks session Goal 0.4509 0.4511 0.3209 0.3400 0.5169 0.4160 Positions Shots on 0.3056 0.3056 0.5418 0.3458 0.1872 0.3372 Target Crosses on 0.0984 0.0395 0.0700 0.1153 0.1664 0.0979 Target Corner 0.0564 0.0376 0.0245 0.0425 0.0277 0.0377 Kicks Ball 0.0888 0.1663 0.0428 0.1564 0.1018 0.1018 Possession

The third step is to calculate the Consistency Ratio (CR). If the CR is much in excess of 0.1, then the questionnaires are inconsistent. For CR calculations, there are two steps:

• Calculate the Consistency Index (CI).

23 • Calculate the Consistency Ratio.

CI λ − n CR = and CI = max (4.14) RI n − 1 where n is the number of inputs. Random Index (RI) is the average random consistency index found using a large sample of randomly generated reciprocal matrices with scales 1/9, 1/8,..., 1,..., 8, 9. As calculated by Saaty [51], the number of the inputs and the average RI are shown in Table A.12.

For the calculation of the consistency index, first, we find λmax as follows. For our first input (goal positions) we first need to calculate its λ value by multiplying geometric means with normalized scores.

λinput1:

(1.0000*0.4160)+(1.4768*0.3372)+(4.5844*0.0979)+(8.0018*0.0377)+(5.0776*0.1018) = 2.2289

Then λinput1 = 2.2289/0.4160 = 5.3585.

We calculate all λ values the same way; the values are given below:

  5.3585      5.6001      λinputs =  5.2735       5.1876    5.1726

and λmax= 5.3185 is the average of these λ values.

Then,

5.3185 − 5 CI = = 0.07962. (4.15) 5 − 1

24 CI 0.07962 CR = = = 0.07. (4.16) RI 1.12

In AHP studies, the judgements obtained from the questionnaires are considered inconsistent if the CR is much in excess of 0.1. Our CR is 0.07, thus, our study is consistent.

AHP results helped setting the upper and lower bounds in the AR model. The results are shown in Table 4.5. In this table, weights for each of the input variables are computed in the DEA model. To ﬁnd lower and upper bound values, the minimum and largest values of each weight for all experts are found. For number of goal positions (I1), the minimum and maximum priority among all experts are 0.2875 and 0.4923, respectively. For number of shots on target (I2), the minimum and the maximum priority among experts are 0.1529 and 0.5156, respectively. Let vI1,...,vI5 be the weights for input I1,...,I5 respectively. The ratio vI1/vI2 has a lower bound of 0.5576 (0.2875/0.5156) and an upper bound of 3.2202 (0.4923/0.1529). In that vein, AR bounds for each pair of inputs can be calculated, as shown in Table 4.6. More information about AR bound calculations can be found in Cooper et al. [48].

25 Table 4.5: Priorities of the inputs by the experts. Expert Expert Expert Expert Expert Minimum Maximum 1 2 3 4 5 priority priority Goal positions 0.4313 0.4923 0.2875 0.3604 0.3018 0.2875 0.4923 (I1) Shots on 0.1529 0.3388 0.3733 0.3093 0.5156 0.1529 0.5156 target (I2) Crosses on 0.0823 0.0599 0.1724 0.2133 0.0698 0.0599 0.2133 target (I3) Corner 0.0352 0.0492 0.0313 0.0321 0.0380 0.0313 0.0492 kicks (I4) Ball possession 0.2983 0.0599 0.1356 0.0849 0.0748 0.0599 0.2983 (I5)

Table 4.6: Assurance Region lower and upper bounds for input ratios. Input ratio Lower bound Upper bound

vI1/vI2 0.5576 3.2202

vI1/vI3 1.3474 8.2178

vI1/vI4 5.8479 15.7495

vI1/vI5 0.9636 8.6065

vI2/vI3 0.7166 8.6065

vI2/vI4 3.1100 16.4944

vI2/vI5 0.5124 8.6065

vI3/vI4 1.2187 6.8254

vI3/vI5 0.2008 3.5614

vI4/vI5 0.1048 0.8206

26 Chapter 5

Results

In this section we present and discuss the results of this study. We experimented with two different DEA models (input-oriented CCR model and AR model) by using DEA-Solver Pro [49] for the weekly assessment of team performances. After each week, an estimate about the final league standings of each team was made from the ranking of the teams’ DEA efficiency score obtained by using the season data through that week. Then, we found Pearson correlation coefficients between final league standings (rank) and DEA efficiency ranks of teams by using Minitab [53]. The results of Pearson correlation coefficients (R-square) for each season can found in Appendix A.13 and A.14.

Figure 5.1 shows Pearson correlation coefficients (R-square) between DEA ranks and the final league standings after each week for each season. Moreover, the summary of regression study for CCR and AR models for all seasons are shown in Table 5.1. We can observe that the AR model provides better accuracy than the CCR model. While the correlations are relatively low at the beginning of the season, since they are increasing with time, we could say that a team’s chance of placing in the estimated position becomes more and more likely as weeks go by. Looking at the average of maximum number of efficient teams within each season, 5 teams are considered relatively efficient with CCR but with AR this reduces to 3 teams. Average efficiency scores of AR are also better for all seasons. For instance in the 2014-2015 season, the average is 38.45 for CCR and 47.55 for AR. CCR

27 model generates many zero weights for the selected input variables which may not be reasonable in the context of football when evaluating team’s eﬃciency relative to its peer. In the AR model, however, model does not allow such inconsistency to happen thus letting all performance indicators to contribute to the eﬃciency.

In another experiment, we correlated weekly DEA results with the standing table that realized after each week as seen in Figure 5.2. In the figure, we can compare these results against the final league standing estimations. It is clear that weekly DEA efficiency scores are highly correlated to the immediate league table after the week. However, it is not possible to use early league data for predicting the final table. The more time passes in the league, the better are the final table estimations. This comparison shows that the data cannot be used to predict positions for the weeks too far into the future.

Figure 5.3 provides the progress of the efficiency scores over time four different cases. Here, horizontal axis represents the weeks while vertical axis represents the DEA scores of the AR model. In Graph (a), we show weekly efficiency scores of the top three teams in the final league table and bottom three teams which are relegated to the league in 2013−2014 season. The final team rankings are shown in parentheses next to a team’s name. For top teams in the final league table, the efficiency scores are increasing and approaching 1 as weeks pass. On the contrary, for relegated teams efficiency scores are decreasing with time. As another observation, in each of the analyzed seasons, the relegated teams finished the league with an efficiency score under 0.6.

The progress of the efficiency scores of Konyaspor, in Graph (b) reflects the stellar performance of the team in 2015−2016. In that season, Konyaspor had its best ever finish by placing as the 3rd best team with the highest number of points collected by the team. However, in the first half of the season, Konyaspor had only 7 wins and 5 draws in 17 games. Then, in the second half they won 12 out 17 games with one loss only. As can be seen from Graph (b) in Figure 5.3, the efficiency scores for Konyaspor are increasing with time eventually becoming 1.

28 The efficiency scores of bottom six teams in season 2012−2013 (Elazı˘gspor, Akhisar Belediye Gen¸clikSpor, Kardemir Karabükspor, Medipol Ba¸sak¸sehirFK, Ordus- por and Mersin Idmanyurdu)˙ are shown in Graph (c). The dotted lines belong to the relegated teams. While the efficiency scores at the end of the season are similar in value, teams that were not relegated consistency improved on their scores whereas the scores of relegated teams kept on decreasing with time.

Graph (d) sheds light to the changes in performance of a single team in different seasons. Kayserispor finished in the eleventh position in 2011−2012, then finished 5th in 2012−2013. Then, in 2013−2014 they were relegated. The efficiency scores from these three seasons mirror the changing performance.

29 30

Figure 5.1: Regression on rank: Final league standings vs. DEA estimations. Table 5.1: Descriptive statistics of CCR and AR models. Season CCR AR 2011-2012 Maximum 68 73 Minimum - 1 Average 41.58 42.89 Standard deviation 19.60 23.58 Average number of efficient team 2 1 Maximum number of efficient team 6 3 2012-2013 Maximum 75 82 Minimum - - Average 28.72 34.99 Standard deviation 21.31 24.26 Average number of efficient team 2 1 Maximum number of efficient team 4 3 2013-2014 Maximum 76 77 Minimum 3 1 Average 46.32 50.90 Standard deviation 22.83 22.53 Average number of efficient team 3 2 Maximum number of efficient team 6 3 2014-2015 Maximum 74 75 Minimum 2 8 Average 38.45 47.55 Standard deviation 24.28 21.50 Average number of efficient team 2 1 Maximum number of efficient team 3 2 2015-2016 Maximum 91 91 Minimum 2 5 Average 63.54 66.44 Standard deviation 24.96 22.57 Average number of efficient team 2 1 Maximum number of efficient team 4 4

31 32

Figure 5.2: Weekly vs. ﬁnal league rank estimation. 33

Figure 5.3: Progress of DEA scores for various cases. 5.1 Financial Data

We also had the transfer fee data which have been collected from Transfermarkt web site [54] spent by each team in each season as summarized in Table 5.2. Due to the static nature of the financial data available, it could not be used in our dynamic estimation approach explained earlier. However, we used whole season’s data together with this financial data and correlated the results with the final standings. Consolidated results of the financial analysis of five seasons are shown in Figure 5.4. There is an obvious kink in 2013−2014 with correlations becoming better with each season after that. Interestingly, UEFA introduced Financial Fair Play Regulations in 2013−2014 in order to prevent professional football clubs from getting into financial problems by spending more than they earn which might threaten long term survival. It appears that the clubs started using their money wisely after the regulations rather than spending it inefficiently as before.

Figure 5.4: Financial analysis of football teams for ﬁve seasons.

34 Table 5.2: Descriptive statistics of ﬁnancial data. Season Transfer Fee (Euro) 2011-2012 Maximum 125,350,000 Minimum 15,930,000 Average 49,373,000 Standard Deviation 35,000,000 2012-2013 Maximum 178,700,000 Minimum 11,950,000 Average 59,770,000 Standard Deviation 45,770,000 2013-2014 Maximum 178,230,000 Minimum 14,150,000 Average 59,060,000 Standard Deviation 45,200,000 2014-2015 Maximum 177,480,000 Minimum 21,150,000 Average 56,600,000 Standard Deviation 41,020,000 2015-2016 Maximum 195,380,000 Minimum 22,700,000 Average 69,920,000 Standard Deviation 47,410,000

35 Chapter 6

Conclusion

Performance assessment and control of professional football teams are the key elements for success on the pitch. Managerial teams consisting of a head coach, assistant coaches, fitness trainers, physiotherapists, and analysts try to develop different strategies for every opponent they face in the national or international contest they appear throughout the season. Most important resource at hand is such strategy planning is the player roster in which they try to find the best mix of players against the opponent in terms of collective game statistics. Reflec- tion of these statistics to the game by means of true performance indication and aggregated efficiency assessment of these indicators is the ultimate goal of every manager. Continuous monitoring of games in comparative manner can support the critical decision processes and help to foresee the teams’ future efficiency and rank with respect to competitors. Dynamic efficiency analysis also identifies the abnormal deviations from a team’s performance pattern in the long run. These irregularities can be beneficial in the monitoring of match fixing activities which gained critical attention in the last decade.

This thesis investigates how estimations of final league standings with DEA efficiency measures evolve as the season progresses using Turkish First Division Football League data for five seasons. The analysis was dynamically performed after each week using a very popular non-parametric frontier estimation technique (DEA). This methodology has been applied to football teams that played

36 in Spor Toto Süper Lig between 2011 and 2016. Two different DEA models were experimented with. While one is a standard model the other one makes use of Analytic Hierarchy Process to include expert opinion in efficiency calculations. We have shown that the model that incorporated expert opinion provided better results than a standard model with no such knowledge.

The choice of variables is important in DEA research. We have conducted a correlation analysis to select a subset of variables from among the data available to us. Not all data was useful for the type of study we conducted. Transfer fees paid by teams for players are one of the important variables many researchers consider. However since these fees are paid at the beginning of the season and do not change during the season, they could not be used in our dynamic scheme. The number of spectators also was another piece of data we could not use because of the local bans on attending away games for the opposition teams.

Each using their own set of variables, researchers came to different conclusions regarding the appropriateness of using DEA efficiencies for predicting the final league tables. While research in Hass [10], Espitia-Escuer and Garcia-Cebrian [12] indicates that DEA efficiency is not always related to league results, other researchers such as Barros and Leach [25] found that correlations between points awarded and CCR efficiency scores are statistically supported. Rather than do- ing an analysis with whole season’s data as in other research, we estimated final league standings dynamically after each week and looked into how these estimations change over the season. The prediction accuracy starts out low but improves as the season progresses reaching significant levels towards the end. It is expected that one would not be able to predict all league table positions correctly-although one would wish to be able to do so far gambling purposes. However, results from such analysis can still be beneficial to teams for improving their competitiveness by concentrating on their inefficiencies during the rest of the season as our research indicates. It is a known fact clubs try to improve their performance by identifying their weaknesses and injury related roster gaps by using mid-season transfer window. Such transfer decision can be supported by concentrating on the

37 indicators causing the ineﬃciencies of the teams. It is also important to look into trends in the evolution of the eﬃciency scores in time rather than just a week’s results as increasing or decreasing patterns could be important indicators for the overall success of a team. We highlighted several cases from the Turkish league where the analysis could have helped the teams.

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44 Appendices

45 Appendix A

A.1 Data

Table A.1: Sample data. Week 34 in 2011-2012. Goal Shots Crosses Ball Goal Corner Teams posi- on on possession Ratio kicks tions target target (%) Ankaragücü 0.286 95 108 111 133 43 Antalyaspor 0.762 137 136 194 158 48 Ba¸sak¸sehir 0.980 186 211 177 175 42 Be¸sikta¸s 1.316 182 182 177 188 51 Bursaspor 1.257 172 175 194 172 50 Eski¸sehirspor 1.024 167 175 191 155 49 Fenerbah¸ce 1.794 189 190 140 175 55 Galatasaray 2.875 188 218 176 187 54 Gaziantepspor 1.182 139 171 148 158 52 Gen¸clerbirli˘gi 1.021 150 155 160 137 45 Karabükspor 0.772 149 155 124 139 49 Kayserispor 1.077 139 152 159 168 47 Manisaspor 0.596 135 136 150 149 47 Mersin 0.756 126 144 277 153 43 Idmanyurdu˙ Orduspor 0.824 111 129 182 161 38 Samsunspor 0.766 131 146 170 168 42 Sivasspor 1.056 177 177 199 173 44 Trabzonspor 1.538 198 195 115 168 50

46 Table A.2: Sample data. Week 34 in 2012-2013. Goal Shots Crosses Ball Goal Corner Teams posi- on on possession Ratio kicks tions target target (%) Akhisar 0.818 155 145 157 158 44 Belediyespor Antalyaspor 0.962 157 146 124 143 48 Ba¸sak¸sehir 0.860 133 149 135 187 47 Be¸sikta¸s 1.286 197 196 139 194 49 Bursaspor 1.268 179 172 160 196 49 Elazı˘gspor 0.674 114 101 138 129 48 Eski¸sehirspor 1.200 178 190 194 161 55 Fenerbah¸ce 1.436 191 188 207 227 57 Galatasaray 1.886 187 202 145 184 58 Gaziantepspor 0.840 151 153 148 149 49 Gen¸clerbirli˘gi 0.979 143 154 140 146 47 Karab¨ukspor 0.774 139 175 133 144 47 Kasımpa¸sa 1.297 166 154 151 153 47 Kayserispor 1.089 168 170 122 173 50 Mersin 0.585 115 117 154 136 55 Idmanyurdu˙ Orduspor 0.686 139 139 164 161 46 Sivasspor 0.913 162 171 136 172 45 Trabzonspor 0.951 161 155 130 168 50

47 Table A.3: Sample data. Week 34 in 2013-2014. Goal Shots Crosses Ball Goal Corner Teams posi- on on possession Ratio kicks tions target target (%) Akhisar 0.800 158 160 151 172 46 Belediyespor Antalyaspor 0.739 150 127 128 149 49 Be¸sikta¸s 1.688 176 170 133 181 56 Bursaspor 0.870 190 180 173 211 47 C¸aykur Rizespor 1.000 143 141 101 167 48 Elazı˘gspor 0.613 143 146 150 167 47 Erciyespor 0.680 142 153 145 154 46 Eski¸sehirspor 0.943 146 159 114 182 54 Fenerbah¸ce 2.242 223 235 180 211 56 Galatasaray 1.758 196 200 184 179 53 Gaziantepspor 0.655 145 151 108 159 45 Gen¸clerbirli˘gi 0.907 146 140 124 156 50 Karab¨ukspor 0.971 151 167 148 174 47 Kasımpa¸sa 1.436 199 184 148 166 49 Kayserispor 0.526 167 157 122 175 52 Konyaspor 1.067 162 147 156 152 48 Sivasspor 1.091 169 181 128 137 53 Trabzonspor 1.293 175 191 108 168 46

48 Table A.4: Sample data. Week 34 in 2014-2015. Goal Shots Crosses Ball Goal Corner Teams posi- on on possession Ratio kicks tions target target (%) Akhisar 0.804 129 155 111 114 48 Belediyespor Balıkesirspor 0.696 136 138 105 143 40 Ba¸sak¸sehir 1.633 165 190 127 153 47 Be¸sikta¸s 1.719 187 189 119 172 55 Bursaspor 1.568 229 223 164 183 51 C¸aykur Rizespor 0.745 167 152 132 156 46 Eski¸sehirspor 0.865 132 148 130 151 50 Fenerbah¸ce 2.069 164 181 127 184 50 Galatasaray 1.714 223 204 210 217 58 Gaziantepspor 0.646 196 202 140 190 53 Gen¸clerbirli˘gi 1.070 126 136 138 128 46 Karab¨ukspor 0.688 138 147 124 146 48 Kasımpa¸sa 0.778 137 155 104 170 52 Kayserispor 0.694 196 200 119 144 49 Konyaspor 0.789 139 158 109 187 47 Mersin 1.125 150 168 133 121 49 Idmanyurdu˙ Sivasspor 0.860 182 159 168 171 52 Trabzonspor 1.208 175 186 177 166 51

49 Table A.5: Sample data. Week 34 in 2015-2016. Goal Shots Crosses Ball Goal Corner Teams posi- on on possession Ratio kicks tions target target (%) Akhisar 1.024 132 136 77 120 47 Belediyespor Antalyaspor 1.000 162 162 84 164 50 Ba¸sak¸sehir 1.500 157 163 104 151 50 Be¸sikta¸s 2.143 226 220 116 221 57 Bursaspor 0.855 149 148 128 151 50 C¸aykur Rizespor 0.813 150 145 118 152 46 Eski¸sehirspor 0.619 131 144 76 146 47 Fenerbah¸ce 2.222 221 203 165 219 56 Galatasaray 1.408 206 207 119 170 55 Gaziantepspor 0.620 103 124 73 124 47 Gen¸clerbirli˘gi 1.000 133 131 89 148 46 Kasımpa¸sa 1.250 176 186 117 174 50 Kayserispor 0.610 139 137 83 181 48 Konyaspor 1.333 133 131 77 135 48 Mersin 0.437 119 126 83 155 48 Idmanyurdu˙ Osmanlıspor 1.440 167 177 80 189 46 Sivasspor 0.708 163 150 115 178 51 Trabzonspor 0.678 147 166 136 151 50

50 Table A.6: Correlation coeﬃcient matrix. Shots Passes Crosses Ball Goal Ball Free Assists on on on Tackles Turnovers Corners Possession Positions Touches Kicks Target Target Target (%) Goal 1.00 Positions Assists 0.82 1.00 Shots on 0.96 0.85 1.00 Target Passes on

51 0.81 0.76 0.80 1.00 Target Crosses on 0.68 0.48 0.63 0.57 1.00 Target Ball 0.84 0.78 0.82 0.99 0.56 1.00 Touches Tackles 0.75 0.79 0.78 0.68 0.50 0.71 1.00 Turnovers 0.60 0.55 0.62 0.56 0.38 0.59 0.74 1.00 Corners 0.85 0.59 0.78 0.53 0.54 0.57 0.58 0.60 1.00 Free Kicks 0.13 -0.03 0.11 0.11 -0.25 0.13 0.16 0.50 0.41 1.00 Ball 0.87 0.71 0.83 0.92 0.68 0.93 0.63 0.62 0.70 0.18 1.00 Possession A.2 Analytic Hierarchy Process

Table A.7: Comparison matrix for the inputs by Expert 1. Ball Goal Shots on Crosses on Corner possession positions target target kicks (%) Goal 1 1/7 9 9 9 positions Shots on 7 1 7 9 7 target Crosses on 1/9 1/7 1 1 3 target Corner 1/9 1/9 1 1 1/5 kicks Ball 1/9 1/7 1/3 5 1 possession

Table A.8: Comparison matrix for the inputs by Expert 2. Ball Goal Shots on Crosses on Corner possession positions target target kicks (%) Goal 1 7 5 5 5 positions Shots on 1/7 1 7 9 1/9 target Crosses on 1/5 1/7 1 7 1/9 target Corner 1/5 1/9 1/9 1 1/9 kicks Ball 1/5 9 9 9 1 possession

52 Table A.9: Comparison matrix for the inputs by Expert 3. Ball Goal Shots on Crosses on Corner possession positions target target kicks (%) Goal 1 7 5 9 5 positions Shots on 1/7 1 9 9 9 target Crosses on 1/5 1/9 1 1 1 target Corner 1/9 1/9 1 1 1 kicks Ball 1/5 1/9 1 1 1 possession

Table A.10: Comparison matrix for the inputs by Expert 4. Ball Goal Shots on Crosses on Corner possession positions target target kicks (%) Goal 1 3 1 9 5 positions Shots on 1/3 1 7 7 3 target Crosses on 1 1/7 1 3 7 target Corner 1/9 1/7 1/3 1 1/5 kicks Ball 1/5 1/3 1/7 5 1 possession

53 Table A.11: Comparison matrix for the inputs by Expert 5. Ball Goal Shots on Crosses on Corner possession positions target target kicks (%) Goal 1 1/7 9 9 9 positions Shots on 7 1 7 9 7 target Crosses on 1/9 1/7 1 1 3 target Corner 1/9 1/9 1 1 1/5 kicks Ball 1/9 1/7 1/3 5 1 possession

Table A.12: Random Index Table. n 1 2 3 4 5 6 7 8 9 10 RI 0.00 0.00 0.58 0.90 1.12 1.24 1.32 1.41 1.46 1.49

54 Figure A.1: AHP questionnaire.

55 A.3 Pearson Correlation Coeﬃcients Results

Table A.13: Regression on rank: Final league standings vs. DEA estimations (R-square %) results. Season 2011-2012 2012-2013 2013-2014 2014-2015 2015-2016 Model CCR AR CCR AR CCR AR CCR AR CCR AR Week 1 2.6 0.8 0.0 0.0 3.3 0.7 2.1 14.7 5.4 5.4 Week 2 0.1 1.1 11.9 7.1 29.6 37.4 14.9 17.0 1.7 10.4 Week 3 2.7 4.0 0.3 0.7 21.3 14.2 3.0 21.9 6.7 21.5 Week 4 20.9 21.7 4.3 6.2 3.6 12.8 18.5 22.0 12.0 26.4 Week 5 41.7 32.3 5.7 10.9 20.0 26.3 8.1 14.7 25.3 40.5 Week 6 39.8 40.4 0.6 0.3 9.8 18.2 14.5 26.9 52.5 56.3 Week 7 32.5 28.7 4.8 4.7 16.0 18.9 5.4 8.3 52.9 53.8 Week 8 27.1 18.0 0.9 2.6 12.7 18.5 6.9 12.8 69.3 63.6 Week 9 23.6 22.2 3.8 15.5 16.8 21.8 5.0 22.0 60.5 67.7 Week 10 20.6 20.0 16.7 19.2 27.8 35.4 14.2 36.4 54.0 59.2 Week 11 25.3 19.1 19.5 21.4 38.3 45.2 13.1 28.5 67.4 67.0 Week 12 18.0 16.0 31.4 24.6 44.0 52.0 21.3 32.3 68.7 68.3 Week 13 23.2 17.8 32.3 35.0 26.4 45.8 20.9 51.7 65.3 65.3 Week 14 35.4 28.0 20.9 25.3 37.9 36.9 26.1 46.0 68.7 66.3 Week 15 30.9 25.5 34.4 39.6 47.4 58.0 35.0 41.9 66.4 61.7 Week 16 40.5 34.0 32.1 39.6 52.0 56.3 36.9 52.0 66.1 64.0 Week 17 42.7 39.5 24.5 36.4 59.2 69.7 42.1 59.4 62.7 63.3 Week 18 57.5 52.9 27.0 39.1 61.8 71.0 48.2 59.4 66.1 68.0 Week 19 49.7 48.0 21.7 27.7 62.4 68.0 52.3 62.7 70.0 71.4 Week 20 44.9 58.5 18.5 20.3 68.7 74.5 53.0 61.5 69.4 72.1 Week 21 60.1 61.7 26.8 33.8 63.0 70.7 50.5 53.5 69.4 71.8 Week 22 50.9 56.0 30.3 42.7 64.0 73.8 48.8 54.8 72.1 72.1 Week 23 61.4 64.3 32.0 46.8 62.4 65.3 49.7 53.2 76.0 79.0 Week 24 56.9 64.0 38.1 47.7 59.6 63.7 56.5 68.0 86.1 84.2 Week 25 53.8 62.7 35.9 51.7 54.3 55.1 56.5 61.0 87.3 88.4 Week 26 62.0 65.0 33.5 48.2 56.5 58.9 59.2 68.0 85.8 88.8 Week 27 54.8 65.6 30.7 48.0 71.8 66.0 56.8 68.0 86.1 88.8 Week 28 61.0 71.8 53.7 60.7 66.4 65.1 68.0 73.8 86.4 89.9 Week 29 64.6 69.0 52.3 64.3 65.3 68.7 63.2 63.4 85.3 87.7 Week 30 61.4 69.0 60.5 65.3 66.7 67.0 68.7 73.1 71.0 83.0 Week 31 57.8 62.0 60.1 66.3 68.0 70.0 71.0 72.5 81.3 84.5 Week 32 57.5 72.8 64.0 76.8 76.4 76.8 74.7 73.2 82.4 90.7 Week 33 64.0 73.2 72.8 79.3 72.4 73.9 73.7 71.4 89.2 88.0 Week 34 67.7 72.5 74.6 81.9 69.0 73.9 68.5 70.7 90.8 89.9

56 Table A.14: Regression on rank: Weekly league standings vs. DEA estimations (R-square %) results. Season 2011-2012 2012-2013 2013-2014 2014-2015 2015-2016 Model CCR AR CCR AR CCR AR CCR AR CCR AR Week 1 47.8 83.0 61.2 67.0 55.3 59.6 43.1 67.3 75.8 74.3 Week 2 70.8 89.7 74.5 79.6 72.0 84.3 18.2 45.1 56.8 65.0 Week 3 78.6 86.1 63.1 67.0 67.7 80.4 42.9 48.5 60.8 74.3 Week 4 77.9 83.4 72.7 79.3 52.9 82.0 51.6 54.4 65.2 80.6 Week 5 83.2 88.4 76.1 83.1 59.1 73.2 41.8 46.8 50.9 69.7 Week 6 94.6 95.8 72.5 69.7 56.0 77.8 22.7 41.6 67.7 67.7 Week 7 78.7 81.5 89.3 83.8 62.0 84.3 27.6 38.0 62.7 64.3 Week 8 73.4 77.7 65.3 67.7 62.8 79.1 16.7 24.0 79.5 80.1 Week 9 74.4 81.2 58.0 78.4 72.9 80.2 11.0 32.8 66.0 71.4 Week 10 72.4 76.8 85.7 88.0 87.6 82.4 14.3 34.0 76.3 74.3 Week 11 85.6 80.1 72.3 77.0 88.5 91.1 18.1 33.3 82.0 80.1 Week 12 82.1 81.3 75.3 68.3 82.4 90.3 40.3 49.1 79.6 81.1 Week 13 84.2 85.0 68.3 72.8 76.0 90.5 40.5 69.0 80.8 78.2 Week 14 59.2 64.3 67.6 75.3 87.2 86.0 49.1 68.0 79.3 80.4 Week 15 65.6 72.1 68.9 80.6 80.6 86.9 52.3 60.7 75.7 76.0 Week 16 78.6 86.8 71.0 79.1 83.9 89.2 50.9 65.3 80.4 75.6 Week 17 83.4 92.7 78.2 82.8 80.6 89.6 61.7 73.2 80.2 79.5 Week 18 81.5 85.7 77.7 77.0 86.1 92.0 58.2 68.0 82.8 82.7 Week 19 84.9 86.1 66.1 73.8 83.9 86.1 49.5 55.1 84.2 84.2 Week 20 81.5 94.3 57.7 64.0 83.5 89.6 48.3 52.0 84.2 82.0 Week 21 84.2 92.7 59.9 68.3 74.3 83.8 58.6 62.3 86.5 85.3 Week 22 66.6 79.7 62.1 75.0 79.8 88.0 56.6 56.0 72.1 72.0 Week 23 86.1 88.8 50.1 67.7 71.4 78.8 56.3 55.7 84.5 86.1 Week 24 78.6 88.4 64.0 76.8 57.7 64.0 68.0 75.7 93.1 90.0 Week 25 80.1 85.3 56.5 76.3 57.1 56.0 66.7 65.0 88.0 87.2 Week 26 86.5 89.6 63.4 79.3 69.4 70.7 71.0 76.8 89.2 84.2 Week 27 80.8 87.2 53.2 74.8 80.5 74.5 70.3 77.5 86.5 85.0 Week 28 78.2 87.6 66.7 79.7 77.1 75.1 75.1 77.3 83.1 82.7 Week 29 69.7 76.0 62.0 78.0 63.7 69.7 68.4 68.7 89.4 87.6 Week 30 64.6 75.7 65.3 75.0 72.8 71.0 72.0 74.1 76.1 78.2 Week 31 69.4 71.4 74.3 82.3 69.4 71.1 73.8 75.3 83.1 86.5 Week 32 67.3 81.5 71.4 86.1 74.0 74.6 77.5 74.6 86.0 93.4 Week 33 70.0 78.2 75.0 84.2 72.8 73.5 74.0 74.3 88.0 88.8 Week 34 67.7 72.5 74.6 81.9 69.0 73.9 68.4 70.7 90.8 89.9